
Contrary to the claim made in [1]}, invariance only under the Carrollian boost (and space-time translation) does not always permit a Belinfante-improvement to a vanishing \(T^x_{\hspace{4.2679pt}t}\)  component. This result is in agreement with the conclusion made in [2]}.

Rather, it is the TSCT symmetry that guarantees \(T^x_{\hspace{4.2679pt}t}=0\) .

Moreover, the conditions for the TSCT invariance include the requirement of the Carrollian boost symmetry. Thus, TSCT invariance implies Carrollian boost invarinace but the converse is not true.

